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C4×C22⋊D587 #34037582

order18784
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D587

Splittings

FittingC22×C4×C587 ⋊ C2
SylowC587 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D587
commutatorC2×C587C22×C4
FrattiniC22C22×D587
FittingC22×C4×C587C2
socle, cosocleC22×C587C23
prime radicalC2×C22⋊D587C2
hypercenterC22×C4D587
hypocenterC587C4×D4
LCSG ▷ C2×C587 ▷ C587
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9392

Conjugacy classes & character table

4708 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C22⋊D587)⋊C8, C8×C22⋊D587, #49177148, …
maximal normal subgroup of(C22⋊D587)⋊C8, C8×C22⋊D587, #49177148, …
maximal quotient ofC4×C22⋊Dic587, C4×(C2×D587)⋊C4, C4×Dic587⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18784, 107);